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On the numerical implementation of variational arbitrary Lagrangian–Eulerian (VALE) formulations

Mosler, J. and Ortiz, M. (2006) On the numerical implementation of variational arbitrary Lagrangian–Eulerian (VALE) formulations. International Journal for Numerical Methods in Engineering, 67 (9). pp. 1272-1289. ISSN 0029-5981. doi:10.1002/nme.1621.

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This paper is concerned with the implementation of variational arbitrary Lagrangian–Eulerian formulations, also known as variational r-adaption methods. These methods seek to minimize the energy function with respect to the finite-element mesh over the reference configuration of the body. We propose a solution strategy based on a viscous regularization of the configurational forces. This procedure eliminates the ill-posedness of the problem without changing its solutions, i.e. the minimizers of the regularized problems are also minimizers of the original functional. We also develop strategies for optimizing the triangulation, or mesh connectivity, and for allowing nodes to migrate in and out of the boundary of the domain. Selected numerical examples demonstrate the robustness of the solution procedures and their ability to produce highly anisotropic mesh refinement in regions of high energy density.

Item Type:Article
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Ortiz, M.0000-0001-5877-4824
Additional Information:© 2006 John Wiley & Sons. Received 24 June 2005. Revised 11 November 2005. Accepted 16 November 2005. Support from the DoE through Caltech’s ASC/ASAP Center for the Simulation of the DynamicResponse of Solids is gratefully acknowledged. JM is also grateful for support from the Deutsche Forschungsgemeinschaft (DFG) under contract/grant number: Mo 1389/1-1.
Funding AgencyGrant Number
Department of Energy (DOE)UNSPECIFIED
Deutsche Forschungsgemeinschaft (DFG)Mo 1389/1-1
Issue or Number:9
Record Number:CaltechAUTHORS:20171128-102503230
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Official Citation:Mosler, J. and Ortiz, M. (2006), On the numerical implementation of variational arbitrary Lagrangian–Eulerian (VALE) formulations. Int. J. Numer. Meth. Engng., 67: 1272–1289. doi:10.1002/nme.1621
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:83502
Deposited By: Lydia Suarez
Deposited On:30 Nov 2017 00:30
Last Modified:15 Nov 2021 19:58

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